Animation nodes "object attribute input" color is not updating
You're looking at the wrong color. The object.color attribute refers to the object's viewport display color :

If you want to get the particular value of an input socket of a particular node in the node tree of a particular material, you need to use :
material.node_tree.nodes.get(&quot;Principled BSDF&quot;).inputs[0].default_value
I suggest using an Expression node to do it. Example :

Result :

Another way to do it, is to link the object viewport color to your principled bsdf. Then you can keep your AN tree :